# Area of a Triangle - Heron's Formula

So what do you do if you only know the three side lengths?

There are just two steps.

**Step 1: Calculate half the perimeter of the triangle and call it s.**

**Step 2: Use the s in the following formula:**

Let's use the formula to determine the area of the triangle above.

Step 1: The perimeter of the triangle is equal to 12 + 22 + 16 = 50

Therefore, the s value is half of 50 or 25.

Step 2: Replace the s in the area formula with 25 and solve.

A =

A =

A =

A = 93.7 m

Therefore, the s value is half of 50 or 25.

Step 2: Replace the s in the area formula with 25 and solve.

A =

A =

A =

A = 93.7 m

^{2}Here are a couple more example to try.

**Example 1:**

**Step 1: Determine half the perimeter.**

**s =**

**Step 2: Use the s in Heron's formula.**

A =

A =

A =

A =

A =

**A = 24 units**^{2}Now, this triangle does give the base and height. So let's compare our work to the formula you might be more familiar with using to solve.

**A =**

**A =**

**A = 24 units**

^{2}Here we have the same answer as we got from using Heron's method.

**Example 2:**

**Step1: Determine half the perimeter.**

**s =**

**s =**

**s = 15.5**

**Step 2: Use the s in Heron's formula.**

**A =**

**A =**

**A =**

**A = 33.7 mm**

^{2}When the solution is not rational, the answer can be rounded. In this example, we rounded to the nearest tenth.

**Let's Review**

If you are given the three sides of a triangle, you can use the perimeter and Heron's formula to determine the area. There are just two steps.

**Step 1: Determine half the perimeter.**

**Step 2: Use the three side lengths and the half perimeter in Heron's formula.**

Some of the areas will be irrational numbers. That means that they cannot be represented as a fraction. Instead they are decimals that never end and never repeat. When this happens, the area can be rounded to whatever place value you may have been asked for.

Related Links:Math Geometry Triangles Geometry Practice Test: Types of Triangles Area of Triangle Perimeter of the Triangle Area of a Triangle Worksheets |